Some excellent points & posts have been made already, and I'll echo some of them here.
As it happens, I have the 13", and love it. Currently, it is my only computer, and I love the quality of the screen, the blazing fast speed of the SSD drive, and the fantastic portability of the device, which matters, as I travel quite a bit. A terrific computer, and one that you can easily use as a sole computer.
The 13" MBA is a superb compromise between a very portable computer, yet still comes with an excellent screen. With the 11", you are getting an exceptionally portable computer, but at the cost of sacrificing some screen space. So, the first question your mum needs to ask is how portable does she need a computer to be?
Now, I love the 11", and one day plan to buy one. However, it is not a computer I would use as a sole computer - I would need to have a second computer with a larger screen which I would use as my main work computer.
Other questions your mum needs to think about include her age (eyes get more strained as you age), and, also her eyesight. I wear glasses, and small screens strain (and stress) my eyes. Comfort and ease matter as much as portability, especially as you age, and, above all, if you are using a computer screen for work purposes (for example, my work requires a lot of writing), or using it to view movies. Scrunching up your eyes to peer at a screen is no fun at all.